If you’re a science geek who likes the “why” questions (why does the universe exist? why does time run in one direction only?) these articles are worth checking out. I have some thoughts about these articles, but I’ll let you read the originals before diving into specifics.

Back? Good.

So these articles are interesting and all, but they’re kind of vague and some of them are actually misleading, so here are some thoughts on all that. (Gordon Smith, if you are out there, please read this and correct anything I get wrong.)

One of the interesting facts of the universe is that it started out in a state with very low entropy. No one knows why. Note that this is not the same thing as saying that it started very very small. Small things can have low entropy or high entropy. In fact, pound for pound, black holes have the most entropy of all. So not only was the early universe very small, it was also a very special kind of small thing with extremely low entropy.

Why is this important? Well, the second law of thermodynamics is predicated on the universe starting out in a low entropy state. Contrary to popular opinion, the second law doesn’t say that entropy increases forever. What it says is that entropy tends to get bigger until you reach a state of near maximum entropy, at which time things basically stay the same.

Example: If I take a pail of water and add a drop of red food dye, it tends to spread out. But once it has spread out evenly, it just stays that way.

The second law is important because that’s what causes our universe to be interesting. In fact, life cannot exist in a high entropy world. In order to maintain the structure and order inherent in our bodies, we need to continually consume energy and spit out heat, which is only possible when we have a low entropy world to spit that heat out into.

To summarize: the early universe was an extremely low entropy state. If you were just picking states randomly, you would be extremely unlikely to arrive at such a state. Because of this, one of the most important questions in cosmology is to ask ourselves why the early universe had such low entropy.

One hypothesis is that it happend “by chance”. That sounds like a crazy argument, but once you dive into it, the argument is not 100% crazy.

Let’s go back to the analogy of the red food dye in the pail of water. It is extremely unlikely for all of the red food dye to be concentrated in a single “drop”. But if you sat there and stared at the pail for an infinite amount of time, it would eventually happen by pure chance.

In the same way, imagine that you were lucky enough to be an observer sitting outside the entire system and you had an infinite amount of time to observe things. (Yes, I know that “time” is a concept that only makes sense within the universe itself, but bear with me.)

Maybe little universes sprout up from time to time and collapse again. And almost all of these universes are, indeed, high entropy universes. But if you have an infinite amount of time to sit around, you will eventually see a low entropy universe arise by pure chance. One estimate of the initial entropy says that the chance of randomly arriving at such a state are 1 in 10^10^123, which is to say it is very very unlikely. But given an infinite number of tries, it will eventually happen.

“So what?” you say. “Isn’t this just monkeys typing Shakespeare?” This is where the anthropic principle comes in.

Remember that life itself can’t exist in high entropy universes. So as you look at these little universes coming and going, you find that 99.9999999…% of them are extremely boring. Nothing happens inside them.

But in the few universes that have a low entropy initial state, you find that interesting stuff happens. Stars form. Life exists.

And as you look inside the tiny fraction of universes that contain intelligent life, you find that scientists are saying things like “gee… that’s funny… according to my calculations, there is a 99.99999999….% probability that the universe should a be high entropy, boring place. So what gives?”

So maybe the argument that our universe started out with low entropy “by chance” is not so crazy after all. Maybe new universes are springing up all the time, but it’s only the low entropy ones that support intelligent life.

This kind of argument relies on something called “the anthropic principle”, which says that it is ok to explain strange facts about our universe if they are necessary to support life (using the argument above). Not all scientists are 100% comfortable with the anthropic principle, but it’s not completely crazy.

With me so far? Wow. Ok, now on to the current discussion about floating brains.

A good scientist will test a hypothesis by seeing if there is any way to knock it down, so let’s try to knock it down.

The hypothesis above says that even though the initial state of the universe is extremely special, you will (a) eventually find a universe like that if you have an infinite amount of time on your hands, and (b) these are the only universes that can support intelligent life.

The problem with this line of thinking is that 10^10^123 is a HUUUUGGGGEEE number. So even though it is true that you would eventually find a universe like ours, you will also see a whole lot of other strange things.

Let’s do a back of the envelope calculation to see how likely it would be for the initial state of the universe to consist of all the particles in the solar system exactly as we see them today, and nothing else. Gee.. that’s (and I am making up this number) 10^10^80. And gee, a world like that could support life (by definition). Or just to be silly, let’s imagine that the universe only consists of your brain, thinking its thoughts, along with signals that fool it into thinking that there is a world out there to observe. Gee, the probability of a universe like that arising randomly is only 10^10^60! So it’s almost infinitely more likely than the universe we live in today.

By making this type of argument, I don’t think anyone is saying that we are actually brains floating in space. The point of this type of argument is to knock down the hypothesis that the early universe found itself in a low entropy state by “pure chance”. The anthropic argument doesn’t help here, because if you judge by entropy alone, illogical worlds that contain intelligence (like a universe consisting only of a floating brain) are WAY WAY more statistically probable than our own universe.

So all this means is that we need to find a different explanation for why the initial state of the universe had such low entropy. Any ideas? :-)

9 Responses to “Are we just brains floating in space?”

Mate, you are just twisting vague ideas so to fit your pseudo rational position. and anyway, making would-be-educated guesses about probability is irrelevant when you have a one-element sample from a population whose characteristics you are perfectly completely unable to even formulate.
And please … the floating brain stuff, what are your probabilistic estimations deriving from anyway? WAY WAY what ???? WTF are you talking about ???? please elabourate … i would love to read through.

Heh. :-) On the one hand, I agree with you. It doesn’t make sense to talk about probability when you have a one element sample. If you step back, this is the root reason why cosmology is sometimes frowned upon by other branches of physics. Cosmology is the study of why the universe is the way it is. Well, given that we only have one universe to work with, it’s hard to form hypotheses for *why* the universe is the way it is.

So it’s a fool’s errand, but one can try. :-)

It’s as if the universe were made of jillions of grains of sand, and we happened to know that at the beginning of the universe, all the grains of sand were stacked vertically on top of each other. It might not make sense to talk about “the probability” that this happened, but you could certainly talk about how unique this configuration was relative to all the other possible configurations.

To be a little more precise, the estimate for the 10^10^123 probability of the initial state of the universe being “just so” comes from a book by Penrose called “The Road to Reality”. On the one hand, he’s a well respected mathematician who dabbles in physics (having co-authored papers by Hawking, etc.) On the other hand, he’s kind of a nutball, so people have differing opinions about him.

Anyway, Penrose’s formulation of the 10^10^123 estimate is pretty solid, I think, and it comes from the following:

1) Our best picture of the early universe comes from the so-called 2.7K background radiation, which is a remnant of the big bang. By observing it, we know that the early universe was extremely homogeneous.

2) We can approximate the mass of the universe as having ~ 10^80 baryons (particles) in it.

3) Based on our measurments of (1) and our count of (2), we can estimate the entropy of the early universe as ~ 10^8 per baryon, which is 10^88. A staggeringly huge number.

4) Now, let’s estimate the entropy of the final days of the universe. Assume the universe is closed, and will ultimately collapse on itself. The argument doesn’t require that the universe actually does this, but calculating the entropy of black holes is easy, so let’s go with that for now.

5) As the entire universe swallows itself into a gigantic black hole, the entropy can be estimated using the Bekenstein-Hawking formula at 10^123.

6) When it comes to probabilities, what matters is not the entropy but the number of accessible states, so we’re really talking about e^10^88 and e^10^123.

7) For large numbers, e^x ~ 10^x, and powers of 10 are a lot easier to work with, so let’s use them instead.

8) By these estimates, the final macro-state of the universe (a singularity) contains ~10^10^123 accessible states. The initial macro-state of the universe (also a singularity, roughly) contained ~10^10^88 accessible states.

9) The ratio between 10^10^123 and 10^10^88 is roughly 10^10^123, so you can see that there are vastly, vastly more singularities that look like an unordered mess than our initial universe.

So to be precise, we are talking about the observed entropy of the early universe and the volume of phase space that it occupies relative to the total space of all available states.

Now you can’t compute “the probability of a floating brain appearing”, because you need to have some kind of hypothesis of a physical process behind that. But you can talk about the “uniqueness” of that state relative to the “uniqueness” of the state of the big bang. And since there are vastly fewer particles in a human brain than there are in the universe, any theory that attempts to explain the initial state of the universe as a “statistical fluctuation” is going to have to explain why other “special configurations” of the universe (such as a human brain that just “thinks” it is observing the universe) can’t occur through the same statistical process.

“But you can talk about the “uniqueness” of that state relative to the “uniqueness” of the state of the big bang.”

I must admit, this is where I get troubled in all the discussion around Boltzmann’s Brains and it’s disproving of the statistical fluctuation model of the big bang’s entropic state.

What troubles me specifically is that when you compare the uniqueness of A: a universe with many Boltzmann Brains, and B: a universe with us in our galaxy in it, it seems wrong to calculate the uniqueness of each simply by how much more complicated our galaxy/solar system/planet is compared to a floating brain of x trillion atoms. Surely one should compare the uniqueness of each system that lead to the final instance of A or B, and when you compare the systems then I fail to see how a system that ends with floating brains is any less complex than one that ends in a planet with scientists observing all and sundry!

Noah: I see what you mean, but I think this is a case where intuition gets in our way.

To be clear, we are comparing the uniqueness of A: a universe with many Boltzmann Brains, and B: a universe consisting of the initial state of the big bang. We are not comparing it with the complexity of the universe today.

We know that the initial state of the big bang was placed in a highly improbable low entropy state. As an analogy, let’s imagine that a large stack of individual grains of sand had been placed on top of one another in perfect balance, and that this stack of sand reached to the moon.

Now, let’s say that someone comes up with a theory that says that the initial state of the universe might have been created through random fluctuations due to the wind. Maybe this stack of sand grains is part of a much, much bigger sandbox, and given infinite time, a stack like this is *bound* to come up sooner or later, right?

Yes, it’s true that given an infinite amount of time of observing random configurations of sand, that we would probably observe a stack of individual grains of sand that reached up to the moon. However, it is infinitely more likely that a 1 foot tall pyramid would appear. Both are unlikely configurations, but the 1 foot tall pyramid is much more more likely than the stack of sand that reaches to the moon.

Again, we are talking about the “specialness” of the initial state of the universe, not the “specialness” of the current state of the universe.

Sho, OK I think I see what you (and all those cosmologists) are saying a little clearer now but to clarify even more, am I correct in thinking that the theoretical Boltzmann Brains Universe is just that, simply an abstract infinite space with an infinite number of floating brains in it? No planets, no galaxies, no black holes etc… On the other side we have “our” universe with it’s annoyingly unlikely low entropic initial state.

Am I right? If so then I guess I can start to agree, or at least properly comprehend.

The only thing that still bugs me is, okay our universe’s initial low entropy big-bang state is super unlikely, but what kind of initial state would a Boltzmann Brains universe need to pop into existence? Would it not also be radically unlikely? Or is this entirely beside the point! ;-)